Finite Group Databasebeta

← C2×Dic3×C22⋊AGL(1,𝔽5) #14319419

Subgroups — C2×Dic3×C22⋊AGL(1,𝔽5) #14319419

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D5×Dic3C211yesmaximal, characteristic
2C22×#6763C211yesmaximal, characteristic
3C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4C22×Dic3×AGL(1,𝔽5)C212yesmaximal, complemented
5Dic3×C22⋊AGL(1,𝔽5)C218yesmaximal, direct product factor
6C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal, complemented
7C2×C4×C22⋊AGL(1,𝔽5)—31nomaximal, Hall
8C24×C3×D5C2211yescharacteristic
9C23×ΓL(1,𝔽16)C2212yes—
10C23×C3×AGL(1,𝔽5)C2212yes—
11C23×Dic15C411yescharacteristic, complemented
12C23×C5×Dic3C411yescharacteristic, complemented
13C22×D5×Dic3—28no—
14C22×D5×Dic3C414yescomplemented
15C22×D5×Dic3C411yescharacteristic, complemented
16C22×D5×Dic3C411yescharacteristic, complemented
17C22×D5×Dic3C2211yescharacteristic
18C22×D5×Dic3C2214yes—
19C22×D5×Dic3C2211yescharacteristic
20C2×#6763C418yescomplemented
21C2×#6763C2214yes—
22C2×C3×C22⋊AGL(1,𝔽5)C418yescomplemented
23C2×C3×C22⋊AGL(1,𝔽5)C2214yes—
24C2×Dic3×AGL(1,𝔽5)—28no—
25C2×Dic3×AGL(1,𝔽5)C2218yescomplemented
26(C2×AGL(1,𝔽5))⋊Dic3C2218yescomplemented
27C2×Dic3×C22⋊C4—51nomaximal, Hall
28C23×C4×D5—31no—
29C22×C22⋊AGL(1,𝔽5)—31no—
30C22×C22⋊AGL(1,𝔽5)D311yescharacteristic
31C22×C4×AGL(1,𝔽5)—32no—
32C4×C22⋊AGL(1,𝔽5)—38no—
33C2×(C2×AGL(1,𝔽5))⋊C4—32no—
34C24×C3×C5C2×C411yescharacteristic
35C23×C3×D5—24no—
36C23×C3×D5—24no—
37C23×C3×D5C2×C411yescharacteristic
38C23×C3×D5C2×C412yes—
39C23×C3×D5C2×C414yes—
40C23×C3×D5C2×C414yes—
41C23×C3×D5C2312yes—
42C23×C3×D5C2311yescharacteristic
43C22×ΓL(1,𝔽16)—24no—
44C22×ΓL(1,𝔽16)—24no—
45C22×ΓL(1,𝔽16)C2×C418yescomplemented
46C22×ΓL(1,𝔽16)C2314yes—
47C22×C3×AGL(1,𝔽5)—24no—
48C22×C3×AGL(1,𝔽5)—24no—
49C22×C3×AGL(1,𝔽5)C2×C418yescomplemented
50C22×C3×AGL(1,𝔽5)C2314yes—
51C22×Dic15—24no—
52C22×Dic15C2×C411yescharacteristic
53C22×Dic15C2×C411yescharacteristic
54C22×Dic15C2×C414yescomplemented
55C22×C5×Dic3—24no—
56C22×C5×Dic3C2×C411yescharacteristic
57C22×C5×Dic3C2×C411yescharacteristic
58C22×C5×Dic3C2×C414yescomplemented
59C2×D5×Dic3—24no—
60C2×D5×Dic3—24no—
61C2×D5×Dic3—24no—
62C2×D5×Dic3—216no—
63C2×D5×Dic3—216no—
64C2×D5×Dic3C2×C412yes—
65C2×D5×Dic3C2×C412yes—
66C2×D5×Dic3C2×C414yescomplemented
67C2×D5×Dic3C2×C414yescomplemented
68C2×D5×Dic3D418yes—
69C2×D5×Dic3C2312yes—
70C2×D5×Dic3C2312yes—
71#6763C2×C4116yescomplemented
72C3×C22⋊AGL(1,𝔽5)C2×C4116yescomplemented
73Dic3×AGL(1,𝔽5)—216no—
74C24×Dic3—51no—
75C22×C3×C22⋊C4—51no—
76C22×#217—51no—
77C22×C4×Dic3—52no—
78C2×C3⋊#95—52no—
79Dic3×C22⋊C4—58no—
80C24×D5C2×D311yescharacteristic
81C23×AGL(1,𝔽5)—32no—
82C23×AGL(1,𝔽5)C2×D312yes—
83C23×C4×C5—31no—
84C23×Dic5—31no—
85C22×C4×D5—31no—
86C22×C4×D5—34no—
87C22×C4×D5—31no—
88C22×C4×D5—31no—
89C22×C4×D5—31no—
90C22×C4×D5—34no—
91C22×C4×D5—68no—
92C2×C22⋊AGL(1,𝔽5)—38no—
93C2×C22⋊AGL(1,𝔽5)—34no—
94C2×C22⋊AGL(1,𝔽5)Dic318yesdirect product factor
95C2×C22⋊AGL(1,𝔽5)C2×D314yes—
96C2×C4×AGL(1,𝔽5)—38no—
97C2×C4×AGL(1,𝔽5)—68no—
98(C2×AGL(1,𝔽5))⋊C4—38no—
99C2×C4×C22⋊C4—151noSylow
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5C4214yescomplemented
103C23×C3×C5C22×C412yes—
104C23×C3×C5C22×C411yescharacteristic
105C22×C3×D5—22no—
106C22×C3×D5—22no—
107C22×C3×D5—24no—
108C22×C3×D5—24no—
109C22×C3×D5—216no—
110C22×C3×D5—216no—
111C22×C3×D5—24no—
112C22×C3×D5—24no—
113C22×C3×D5C4218yescomplemented
114C22×C3×D5C4214yescomplemented
115C22×C3×D5C22×C412yes—
116C22×C3×D5C22×C414yes—
117C22×C3×D5C22×C414yes—
118C22×C3×D5C22×C411yescharacteristic
119C22×C3×D5C22×C412yes—
120C22×C3×D5C22×C412yes—
121C22×C3×D5C2×D414yes—
122C22×C3×D5#4114yes—
123C22×C3×D5C2411yescharacteristic
124C2×ΓL(1,𝔽16)—216no—
125C2×ΓL(1,𝔽16)—24no—
126C2×ΓL(1,𝔽16)—24no—
127C2×ΓL(1,𝔽16)C22×C418yescomplemented
128C2×C3×AGL(1,𝔽5)—216no—
129C2×C3×AGL(1,𝔽5)—24no—
130C2×C3×AGL(1,𝔽5)—24no—
131C2×C3×AGL(1,𝔽5)C22×C418yescomplemented
132C2×Dic15—22no—
133C2×Dic15—28no—
134C2×Dic15C22⋊C414yescomplemented
135C2×Dic15C22×C412yes—
136C2×Dic15C22×C412yes—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—28no—
139C2×C5×Dic3C22⋊C414yescomplemented
140C2×C5×Dic3C22×C412yes—
141C2×C5×Dic3C22×C412yes—
142D5×Dic3—24no—
143D5×Dic3—24no—
144D5×Dic3—28no—
145D5×Dic3—28no—
146D5×Dic3C22⋊C418yescomplemented
147D5×Dic3C2×D418yes—
148C25×C3—51no—
149C23×C3×C4—52no—
150C23×Dic3—51no—
151C23×Dic3—52no—
152C23×Dic3—51no—
153C23×Dic3—51no—
154C23×Dic3—51no—
155C23×Dic3—51no—
156C23×Dic3—54no—
157C23×Dic3—54no—
158C23×Dic3—108no—
159C23×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
160C2×C3×C22⋊C4—54no—
161C2×C3×C22⋊C4—58no—
162C2×#217—54no—
163C2×#217—58no—
164C2×C4×Dic3—58no—
165C2×C4×Dic3—108no—
166C3⋊#95—58no—
167C24×C5C4×D311yescharacteristic
168C23×D5—24no—
169C23×D5—24no—
170C23×D5C4×D312yes—
171C23×D5C4×D311yescharacteristic
172C23×D5C4×D314yes—
173C23×D5C2×Dic314yes—
174C23×D5C22×D312yes—
175C23×D5C22×D311yescharacteristic
176C22×AGL(1,𝔽5)—24no—
177C22×AGL(1,𝔽5)—24no—
178C22×AGL(1,𝔽5)—38no—
179C22×AGL(1,𝔽5)—34no—
180C22×AGL(1,𝔽5)—64no—
181C22×AGL(1,𝔽5)—64no—
182C22×AGL(1,𝔽5)C2×Dic318yescomplemented
183C22×AGL(1,𝔽5)C22×D314yes—
184C22×C4×C5—31no—
185C22×C4×C5—31no—
186C22×C4×C5—34no—
187C22×C4×C5—64no—
188C22×Dic5—31no—
189C22×Dic5—31no—
190C22×Dic5—34no—
191C22×Dic5—64no—
192C2×C4×D5—32no—
193C2×C4×D5—38no—
194C2×C4×D5—32no—
195C2×C4×D5—32no—
196C2×C4×D5—34no—
197C2×C4×D5—34no—
198C2×C4×D5—32no—
199C2×C4×D5—616no—
200C2×C4×D5—616no—
201C2×C4×D5—64no—
202C2×C4×D5—64no—
203C2×C4×D5—64no—
204C22⋊AGL(1,𝔽5)—316no—
205C22⋊AGL(1,𝔽5)C2×Dic3116yesdirect product factor
206C4×AGL(1,𝔽5)—616no—
207C24×C4—151no—
208C22×C22⋊C4—51no—
209C22×C22⋊C4—151no—
210C22×C42—152no—
211C4×C22⋊C4—158no—
212C2×#95—152no—
213C22×C3×C5—22no—
214C22×C3×C5—22no—
215C22×C3×C5—28no—
216C22×C3×C5C2×C4212yes—
217C22×C3×C5C2×C4214yescomplemented
218C22×C3×C5C2×C22⋊C412yes—
219C22×C3×C5#11712yes—
220C22×C3×C5C23×C411yescharacteristic
221C2×C3×D5—22no—
222C2×C3×D5—22no—
223C2×C3×D5—28no—
224C2×C3×D5—28no—
225C2×C3×D5—28no—
226C2×C3×D5—216no—
227C2×C3×D5C2×C4212yes—
228C2×C3×D5C2×C4214yescomplemented
229C2×C3×D5C2×C22⋊C412yes—
230C2×C3×D5#11712yes—
231C2×C3×D5C4×D418yes—
232C2×C3×D5C4×D418yes—
233C2×C3×D5C23×C411yescharacteristic
234C2×C3×D5C23×C411yescharacteristic
235C2×C3×D5C22×D412yes—
236C2×C3×D5C2×#4112yes—
237ΓL(1,𝔽16)—28no—
238C3×AGL(1,𝔽5)—28no—
239Dic15—22no—
240Dic15C2×C22⋊C414yescomplemented
241C5×Dic3—22no—
242C5×Dic3C2×C22⋊C414yescomplemented
243C24×C3—51no—
244C24×C3—54no—
245C24×C3—54no—
246C24×C3—52no—
247C24×C3—52no—
248C24×C3—51no—
249C24×C3—104no—
250C24×C3—104no—
251C24×C3C2×AGL(1,𝔽5)11yescharacteristic
252C22×C3×C4—54no—
253C22×C3×C4—58no—
254C22×C3×C4—104no—
255C22×C3×C4—104no—
256C22×Dic3—24no—
257C22×Dic3—51no—
258C22×Dic3—58no—
259C22×Dic3—52no—
260C22×Dic3—52no—
261C22×Dic3—54no—
262C22×Dic3—58no—
263C22×Dic3—51no—
264C22×Dic3—54no—
265C22×Dic3—52no—
266C22×Dic3—52no—
267C22×Dic3—54no—
268C22×Dic3—54no—
269C22×Dic3—104no—
270C22×Dic3—1016no—
271C22×Dic3—1016no—
272C22×Dic3—104no—
273C22×Dic3—104no—
274C22×Dic3—104no—
275C22×Dic3—104no—
276C22×Dic3—104no—
277C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
278C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
279C22×Dic3C2×AGL(1,𝔽5)14yescomplemented
280C3×C22⋊C4—516no—
281#217—516no—
282C4×Dic3—1016no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5C4×Dic314yescomplemented
286C23×C5C2×C4×D312yes—
287C23×C5C2×C4×D311yescharacteristic
288C22×D5—22no—
289C22×D5—22no—
290C22×D5—24no—
291C22×D5—24no—
292C22×D5—216no—
293C22×D5—216no—
294C22×D5—24no—
295C22×D5—24no—
296C22×D5C4×Dic318yescomplemented
297C22×D5C4×Dic314yescomplemented
298C22×D5C2×C4×D312yes—
299C22×D5C2×C4×D314yes—
300C22×D5C2×C4×D311yescharacteristic
301C22×D5C2×C4×D312yes—
302C22×D5D3×D414yes—
303C22×D5#23714yes—
304C22×D5C22×Dic314yes—
305C22×D5C22×Dic312yes—
306C22×D5C23×D311yescharacteristic
307C2×AGL(1,𝔽5)—216no—
308C2×AGL(1,𝔽5)—24no—
309C2×AGL(1,𝔽5)—24no—
310C2×AGL(1,𝔽5)—38no—
311C2×AGL(1,𝔽5)—616no—
312C2×AGL(1,𝔽5)—64no—
313C2×AGL(1,𝔽5)—64no—
314C2×AGL(1,𝔽5)C22×Dic318yescomplemented
315C2×C4×C5—34no—
316C2×C4×C5—32no—
317C2×C4×C5—32no—
318C2×C4×C5—68no—
319C2×C4×C5—62no—
320C2×Dic5—34no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—68no—
324C2×Dic5—62no—
325C4×D5—38no—
326C4×D5—38no—
327C4×D5—68no—
328C4×D5—68no—
329C4×D5—64no—
330C4×D5—64no—
331C25—51no—
332C23×C4—31no—
333C23×C4—52no—
334C23×C4—151no—
335C23×C4—151no—
336C23×C4—154no—
337C23×C4—151no—
338C23×C4—154no—
339C23×C4—151no—
340C23×C4—152no—
341C23×C4—151no—
342C23×C4—308no—
343C2×C22⋊C4—58no—
344C2×C22⋊C4—54no—
345C2×C22⋊C4—154no—
346C2×C22⋊C4—158no—
347C2×C42—158no—
348C2×C42—308no—
349#95—158no—
350C2×C3×C5—24no—
351C2×C3×C5C4×C22⋊C414yescomplemented
352C2×C3×C5C22×C4211yescharacteristic
353C2×C3×C5C22×C22⋊C411yescharacteristic
354C2×C3×C5C2×#11711yescharacteristic
355C3×D5—24no—
356C3×D5C4×C22⋊C414yescomplemented
357C3×D5C2×C4×D412yes—
358C3×D5C2×C4×D412yes—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—52no—
362C23×C3—52no—
363C23×C3—54no—
364C23×C3—54no—
365C23×C3—51no—
366C23×C3—51no—
367C23×C3—54no—
368C23×C3—58no—
369C23×C3—54no—
370C23×C3—54no—
371C23×C3—52no—
372C23×C3—104no—
373C23×C3—104no—
374C23×C3—104no—
375C23×C3—104no—
376C23×C3—1016no—
377C23×C3—1016no—
378C23×C3—102no—
379C23×C3—102no—
380C23×C3C4×AGL(1,𝔽5)14yescomplemented
381C23×C3C22×AGL(1,𝔽5)12yes—
382C23×C3C22×AGL(1,𝔽5)11yescharacteristic
383C2×C3×C4—58no—
384C2×C3×C4—104no—
385C2×C3×C4—104no—
386C2×C3×C4—1016no—
387C2×Dic3—22no—
388C2×Dic3—28no—
389C2×Dic3—54no—
390C2×Dic3—52no—
391C2×Dic3—58no—
392C2×Dic3—58no—
393C2×Dic3—58no—
394C2×Dic3—52no—
395C2×Dic3—108no—
396C2×Dic3—104no—
397C2×Dic3—104no—
398C2×Dic3—108no—
399C2×Dic3—104no—
400C2×Dic3—104no—
401C2×Dic3—1016no—
402C2×Dic3—102no—
403C2×Dic3—108no—
404C2×Dic3C22⋊AGL(1,𝔽5)14yesdirect product factor
405C2×Dic3C22×AGL(1,𝔽5)12yes—
406C2×Dic3C22×AGL(1,𝔽5)12yes—
407C22×C5—28no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5#87712yes—
411C22×C5D3×C22⋊C412yes—
412C22×C5C2×C4×Dic312yes—
413C22×C5C2×C4×Dic314yescomplemented
414C22×C5C22×C4×D311yescharacteristic
415C2×D5—28no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—216no—
419C2×D5—28no—
420C2×D5—28no—
421C2×D5#87712yes—
422C2×D5D3×C22⋊C412yes—
423C2×D5#67⋊C418yes—
424C2×D5C2×C4×Dic312yes—
425C2×D5C2×C4×Dic314yescomplemented
426C2×D5D4×Dic318yes—
427C2×D5C22×C4×D311yescharacteristic
428C2×D5C2×D3×D412yes—
429C2×D5C2×#23712yes—
430C2×D5C23×Dic311yescharacteristic
431AGL(1,𝔽5)—28no—
432AGL(1,𝔽5)—68no—
433C4×C5—34no—
434C4×C5—62no—
435Dic5—34no—
436Dic5—62no—
437C24—51no—
438C24—54no—
439C24—54no—
440C24—52no—
441C24—52no—
442C24—51no—
443C24—104no—
444C24—104no—
445C24D3×AGL(1,𝔽5)11yescharacteristic
446C22×C4—31no—
447C22×C4—34no—
448C22×C4—31no—
449C22×C4—54no—
450C22×C4—58no—
451C22×C4—64no—
452C22×C4—104no—
453C22×C4—104no—
454C22×C4—152no—
455C22×C4—158no—
456C22×C4—152no—
457C22×C4—152no—
458C22×C4—154no—
459C22×C4—154no—
460C22×C4—152no—
461C22×C4—151no—
462C22×C4—154no—
463C22×C4—158no—
464C22×C4—154no—
465C22×C4—151no—
466C22×C4—304no—
467C22×C4—3016no—
468C22×C4—3016no—
469C22×C4—304no—
470C22×C4—304no—
471C22×C4—304no—
472C22×C4—304no—
473C22×C4—304no—
474C22⋊C4—516no—
475C22⋊C4—1516no—
476C42—3016no—
477C3×C5C2×C4×C22⋊C411yescharacteristic, complemented, Hall
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—28no—
481C22×C3—52no—
482C22×C3—51no—
483C22×C3—51no—
484C22×C3—52no—
485C22×C3—52no—
486C22×C3—52no—
487C22×C3—52no—
488C22×C3—58no—
489C22×C3—58no—
490C22×C3—54no—
491C22×C3—108no—
492C22×C3—108no—
493C22×C3—1016no—
494C22×C3—102no—
495C22×C3—102no—
496C22×C3—108no—
497C22×C3C2×C4×AGL(1,𝔽5)12yes—
498C22×C3C2×C4×AGL(1,𝔽5)14yescomplemented
499C22×C3#413012yes—
500C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
501C22×C3C23×AGL(1,𝔽5)11yescharacteristic
502C3×C4—108no—
503Dic3—22no—
504Dic3—54no—
505Dic3—108no—
506Dic3—102no—
507Dic3C2×C22⋊AGL(1,𝔽5)14yesdirect product factor
508C2×C5—24no—
509C2×C5Dic3×C22⋊C414yescomplemented
510C2×C5C2×#87711yescharacteristic
511C2×C5C2×D3×C22⋊C411yescharacteristic
512C2×C5C22×C4×Dic311yescharacteristic
513D5—24no—
514D5Dic3×C22⋊C414yescomplemented
515D5C2×#67⋊C412yes—
516D5C2×D4×Dic312yes—
517C23—22no—
518C23—22no—
519C23—52no—
520C23—52no—
521C23—54no—
522C23—54no—
523C23—51no—
524C23—51no—
525C23—54no—
526C23—54no—
527C23—54no—
528C23—58no—
529C23—52no—
530C23—104no—
531C23—104no—
532C23—104no—
533C23—104no—
534C23—1016no—
535C23—1016no—
536C23—102no—
537C23—102no—
538C23Dic3×AGL(1,𝔽5)14yescomplemented
539C23C2×D3×AGL(1,𝔽5)12yes—
540C23C2×D3×AGL(1,𝔽5)11yescharacteristic
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—58no—
545C2×C4—68no—
546C2×C4—62no—
547C2×C4—104no—
548C2×C4—104no—
549C2×C4—1016no—
550C2×C4—158no—
551C2×C4—158no—
552C2×C4—154no—
553C2×C4—152no—
554C2×C4—158no—
555C2×C4—152no—
556C2×C4—308no—
557C2×C4—308no—
558C2×C4—304no—
559C2×C4—304no—
560C2×C4—308no—
561C2×C4—304no—
562C2×C4—304no—
563C2×C4—3016no—
564C2×C4—302no—
565C2×C3—24no—
566C2×C3—52no—
567C2×C3—52no—
568C2×C3—54no—
569C2×C3—104no—
570C2×C3C4×C22⋊AGL(1,𝔽5)14yescomplemented
571C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
572C2×C3C2×#413011yescharacteristic
573C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
574C5C2×Dic3×C22⋊C411yescharacteristic, complemented, Sylow
575C22—22no—
576C22—22no—
577C22—28no—
578C22—51no—
579C22—51no—
580C22—52no—
581C22—52no—
582C22—52no—
583C22—52no—
584C22—52no—
585C22—58no—
586C22—58no—
587C22—54no—
588C22—108no—
589C22—108no—
590C22—1016no—
591C22—102no—
592C22—102no—
593C22—108no—
594C22C2×Dic3×AGL(1,𝔽5)12yes—
595C22C2×Dic3×AGL(1,𝔽5)14yescomplemented
596C22#9192312yes—
597C22D3×C22⋊AGL(1,𝔽5)12yes—
598C22C22×D3×AGL(1,𝔽5)11yescharacteristic
599C4—34no—
600C4—62no—
601C4—108no—
602C4—154no—
603C4—308no—
604C4—302no—
605C3C2×C4×C22⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
606C2—24no—
607C2—52no—
608C2—52no—
609C2—54no—
610C2—104no—
611C2Dic3×C22⋊AGL(1,𝔽5)14yesdirect product factor
612C2C22×Dic3×AGL(1,𝔽5)11yescharacteristic
613C2C2×#9192311yescharacteristic
614C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C24

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C22×Dic3×AGL(1,𝔽5)C2semidirect
5. Dic3×C22⋊AGL(1,𝔽5)C2direct (N × H)
6. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
11. C23×Dic15C4semidirect
12. C23×C5×Dic3C4semidirect
14. C22×D5×Dic3C4semidirect
15. C22×D5×Dic3C4semidirect
16. C22×D5×Dic3C4semidirect
20. C2×#6763C4semidirect
22. C2×C3×C22⋊AGL(1,𝔽5)C4semidirect
25. C2×Dic3×AGL(1,𝔽5)C22semidirect
26. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
45. C22×ΓL(1,𝔽16)C2×C4semidirect
49. C22×C3×AGL(1,𝔽5)C2×C4semidirect
54. C22×Dic15C2×C4semidirect
58. C22×C5×Dic3C2×C4semidirect
66. C2×D5×Dic3C2×C4semidirect
67. C2×D5×Dic3C2×C4semidirect
71. #6763C2×C4semidirect
72. C3×C22⋊AGL(1,𝔽5)C2×C4semidirect
94. C2×C22⋊AGL(1,𝔽5)Dic3direct (N × H)
102. C23×C3×C5C42semidirect
113. C22×C3×D5C42semidirect
114. C22×C3×D5C42semidirect
127. C2×ΓL(1,𝔽16)C22×C4semidirect
131. C2×C3×AGL(1,𝔽5)C22×C4semidirect
134. C2×Dic15C22⋊C4semidirect
139. C2×C5×Dic3C22⋊C4semidirect
146. D5×Dic3C22⋊C4semidirect
159. C23×Dic3AGL(1,𝔽5)semidirect
182. C22×AGL(1,𝔽5)C2×Dic3semidirect
205. C22⋊AGL(1,𝔽5)C2×Dic3direct (N × H)
217. C22×C3×C5C2×C42semidirect
228. C2×C3×D5C2×C42semidirect
240. Dic15C2×C22⋊C4semidirect
242. C5×Dic3C2×C22⋊C4semidirect
279. C22×Dic3C2×AGL(1,𝔽5)semidirect
285. C23×C5C4×Dic3semidirect
296. C22×D5C4×Dic3semidirect
297. C22×D5C4×Dic3semidirect
314. C2×AGL(1,𝔽5)C22×Dic3semidirect
351. C2×C3×C5C4×C22⋊C4semidirect
356. C3×D5C4×C22⋊C4semidirect
380. C23×C3C4×AGL(1,𝔽5)semidirect
404. C2×Dic3C22⋊AGL(1,𝔽5)direct (N × H)
413. C22×C5C2×C4×Dic3semidirect
425. C2×D5C2×C4×Dic3semidirect
477. C3×C5C2×C4×C22⋊C4semidirect
498. C22×C3C2×C4×AGL(1,𝔽5)semidirect
507. Dic3C2×C22⋊AGL(1,𝔽5)direct (N × H)
509. C2×C5Dic3×C22⋊C4semidirect
514. D5Dic3×C22⋊C4semidirect
538. C23Dic3×AGL(1,𝔽5)semidirect
570. C2×C3C4×C22⋊AGL(1,𝔽5)semidirect
574. C5C2×Dic3×C22⋊C4semidirect
595. C22C2×Dic3×AGL(1,𝔽5)semidirect
605. C3C2×C4×C22⋊AGL(1,𝔽5)semidirect
611. C2Dic3×C22⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×D5×Dic32
C22×#67632
C22×C3×C22⋊AGL(1,𝔽5)2
C22×Dic3×AGL(1,𝔽5)2
Dic3×C22⋊AGL(1,𝔽5)2
C2×(C2×AGL(1,𝔽5))⋊Dic32
C2×C4×C22⋊AGL(1,𝔽5)3
C2×Dic3×C22⋊C45